Question

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is ______.

विकल्प

• 9

• 15

• `sqrt(353)`

• 25

Answer 1

In the given figure, AB and AC are tangents to a circle with centre O and radius 8 cm. If OA = 17 cm, then the length of AC (in cm) is 15.

Explanation:

Draw OC to the point of contact C.

OC = 8 is perpendicular to tangent AC, so triangle OCA is right-angled.

By Pythagoras, `AC = sqrt(OA^2 - OC^2)` 

= `sqrt(17^2 - 8^2)`

= `sqrt(289 - 64)`

= `sqrt(225)`

= 15